Dualities in two dimensional supersymmetric gauge theories

MasterIn this thesis, we have checked the dualities in two dimensional supersymmetric gauge theories especially focus N=(2,2) on torus T^2. Using localization techniques and Jeffrey Kirwan residue method, one can compute exact partition function of given theory. Via these partition function we have checked the dualites of given theories. Then using these dualities, we extend 2d/4d coupled system and check hopping relation of 2d/4d coupled system. And In N =(0,2) theories we have checked triality, and we expect this trality can be important role of checking dualities in 2d/4d coupled system